Name: 

Write the ordered pairs for the relation. Find the domain and range.

Graph the relation. Find the domain and range.

Make a mapping diagram for the relation.
{(–1, –3), (0, 1), (3, –1), (4, –6)}

Find the domain and range of the relation and determine whether it is a function.

Use the vertical-line test to determine which graph represents a function.

For , .

Suppose and .
Find the value of .

Graph the equation .

Graph the equation by finding the intercepts.

Graph the equation –3x – y = 6.

(6, 12) and (–6, –2)

(, ) and (, )

slope = –8; (–2, –2)

slope = ; (5, –3)

Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).

x = a

through (2, 6) and perpendicular to y = x + 1.

through (–4, 6) and parallel to y = x + 4.

through (–7, –4) and vertical.

–6y = –5x

8y = 7x – 27

The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies directly with the capacity of the gas tank C in gallons.

a.	Find the constant of variation for a car whose range is 341 mi with a gas tank that holds 22 gal.
b.	Write an equation to model the relationship between the range and the capacity of the gas tank.

A leaky valve on the water meter overcharges the residents for one gallon of water in every months. The overcharged amount w varies directly with time t.

a.	Find the equation that models this direct variation.
b.	How many months it will take for the residents to be overcharged for 8 gallons of water?

If y = 166 when x = 83, what is y when x = 23?

If y = 4.8 when x = 2.4, what is y when x = 2.05?

The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 112 miles in 3.5 hours, how many miles will Olivia travel in 8.9 hours at the same constant speed?

A balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model the balloon’s elevation h as a function of time t.

A new candle is 8 inches tall and burns at a rate of 2 inches per hour.

a.	Write an equation that models the height h after t hours.
b.	Sketch the graph of the equation.

A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a function of distance d.

A cannery processed 605 pounds of strawberries in 3.5 hours. The cannery processed 2100 pounds in 10 hours.

a.	Write a linear equation to model the weight of strawberries S processed in T hours.
b.	How many pounds of strawberries can be processed in 12 hours?

A candle is 10 in. tall after burning for 2 hours. After 3 hours, it is in. tall.

a.	Write a linear equation to model the height h of the candle after burning t hours.
b.	Predict how tall the candle will be after burning 6 hours.

Graph the set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation.
{(1, 7), (–2, 1), (3, 13), (–4, –3), (0, 5)}

What is the vertex of the function ?

Match the equation with its graph.

Write two linear equations you can use to graph .

Write two linear equations you can use to graph the equation.

The graph models a train’s distance from a river as the train travels at a constant speed. Which equation best represents the relation?

Write the equation for the translation of .

Graph the equation of y = |x| translated 4 units up.

Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function.

The equation describes a function that is translated from a parent function.

a.	Write the equation of the parent function. Then find the number of units and the direction of translation.
b.	Sketch the graphs of the two functions.

; 4 units down

; 2 units down

Write an equation for the horizontal translation of .

The equation describes a function that is translated from a parent function.

a.	Write the equation of the parent function.
b.	Find the number of units and the direction of translation.
c.	Sketch the graphs of the two functions.

Write the equation that is the translation of left 1 unit and up 2 units.

Graph the function .

Describe the relationship between the graph of and the graph of in terms of a vertical and a horizontal translation. Then graph .

4x – 2y < –3

–3x + y £ 5

A doctor’s office schedules 15-minute appointments and half-hour appointments for weekdays. The doctor limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15-minute appointments x and the number of half-hour appointments y the doctor may have in a week.

An electronics store makes a profit of $20 for every portable DVD player sold and $45 for every DVD recorder sold. The manager’s target is to make at least $180 a day on sales of the portable DVD players and DVD recorders. Write and graph an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r represent the number of DVD recorders.

Write an inequality for the graph.

y < |x + 2| – 2

y ³ |x + 3| – 2

–|x – 1| > y – 5

Graph the relation.

Is the relation {(–2, 5), (–1, 5), (–1, 4), (–1, –3), (–2, 0)} a function? Explain.

Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain.

The area of a round plate is a function of the radius of the circle. Write a function to model the area of a round plate. Evaluate the function for a plate of radius 5.5 in.

Find the slope of the line. Show your work.

Rx + Sy = T

A manufacturing company’s profits are modeled by the equation , where y dollars is the total profit and x is the number of items manufactured. Graph the equation and explain what the x- and y-intercepts represent.

Write the equation of the line that contains the point (8, –3) and is perpendicular to . Graph the equation. Write the equation in standard form. Show your work.

Use the following data: .

a.	Make a scatter plot.
b.	Draw a trend line for your scatter plot.
c.	Write a linear equation for your trend line. Show your work.

Describe the vertical-line test for a graph and tell how it can determine whether a graph represents a function.

Explain how to find the x-coordinate of the vertex of .

Do the values in the table represent a direct variation? Explain your answer.

x	4	5	7
y	13.1	16.3	22.6